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11x^2-10x=11
We move all terms to the left:
11x^2-10x-(11)=0
a = 11; b = -10; c = -11;
Δ = b2-4ac
Δ = -102-4·11·(-11)
Δ = 584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{146}}{2*11}=\frac{10-2\sqrt{146}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{146}}{2*11}=\frac{10+2\sqrt{146}}{22} $
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